There are two downsides: it's at least $20 a month to do it, and having your own mail server really isn't quite a set-it-and-forget-it deal. It requires an amount of attention that wouldn't make sense for a lot of people (or businesses).
I'm surprised by how many businesses (even small ones) don't run their own mail server, or at least have a proper outsourcing arrangement rather than just using a public service. We run our own (well, I run our own...) because we work with banks and all contracts we sign with them have clauses regarding where information from them gets stored and who could possibly have access to it - this is to protect their data in instances where we might be sent (intentionally or otherwise) information about some of their employees or customers. I'm guessing a great many businesses work with clients who have similar concerns so those clauses will be present in contracts that have signed too, so using a "public" service like gmail or hotmail just isn't compatible with them - we can't make any demands to Google about who can access what on their servers or audit them.
No business should use a public service like that and leave the mail on it. This isn't a dig at the public services like gmail, as they provide a valuable resource for those the resource is not wrong for, but they can not provide the accountability I would expect to be able to provide my clients as a business. Businesses should (IMO, and in order of preference) run their own server, use a service that has some contractually enforced security guarantee, or pull down the mail to local systems rather then leaving it on a public server - otherwise they can have no hope at all of controlling who can access their (potentially confidential and sensitive) mail.
Aside from the data security issue there are other potential problems that should be concerned about. If a public services goes down there is nothing you can do to help a fast recovery and you will not be their priority: your services will be available again when it is available again. Also you need to implement a good backup system no matter what you chose - you should not (as many people do) rely on a single service for both your live mail handling and backups.
The $20/month is nothing to a business (or should be), but you are right in that a mail server should never be considered a set-and-forget system so there will be technical resource cost involved with running a mail server and dealing with possible issues like "friendly fire blacklisting" so a reputable outsourcing arrangement would be more cost-/manpower- effective for many small businesses.
FYI: we currently use Zimbra's "community edition", though at some point I'd like to convince the powers that be that using the paid edition would be worth it for the support (there has never been an issue I can't resolve, and there is never likely to be, but I'm not here 24/7 and don't have someone with the right skills to delegate the job to when I'm not around). It is more resource hungry than Postfix+Dovecot+RoundCube though so needs significantly more the linode's $20 VM product to be usable, but I recommend people give it a try as its single install removes the need for you to perform any integration work putting a stack together and the feature set aside from email is no unattractive either.
I had only sorta-kinda considered trying to offer that to a wider audience, but I didn't really think the market for it was that big. I might be wrong.
I am a linode user myself and I was interested in setting up a mail server of my own for personal use, but I will admit I don't know much about it.
Probably my number one time sink on the mail server is, "Where is the email from X that I've been expecting?" A close number two is, "I'm getting too much spam." If you're paying for hosted email from someone else, you can just give them a call and make it their headache. If you're doing your own, it's your own headache, and it's a headache that can easily consume a few hours at a time.
You also should regularly check in with various system and software logs, to make sure that someone isn't trying a novel new attack against the mail server, or that a process isn't struggling for some reason.
Most of the software does a pretty good job of being rock-solid, so I don't find myself having to tune things all the time or nudge dead processes or anything. But, I did find that if I left the mail server alone for a while, then when something did go wrong, it took me a lot longer to resolve it (I think mostly because I'd forgotten where everything was), which is not what I want in a downtime situation.
I think something like this could be valuable to a lot of small to medium companies who atm can't resist subscribing to Google Apps (50,- per user you could have instead). I think with a service like that, the main goal would be to stay as simple as possible while still offering the "Exchange" integration with people's current infrastructure.
I would do the user side web frontend last and concentrate on a simple but empowering foundation plus administration interface first.
Clearly with the PSN breach and all the bad press Google, Apple & Co. are getting with location/mobile I can see a shift in people's minds towards more privacy and security similar to when people started to get used to anti-virus/firewall software.
2011 - Devops galore.